At point K a particle which is at rest starts motion when $t=0$ it moves with a uniform acceleration $f_1$ for a period of $t_1$. Then it decelerates by $f_2$ for a period of $t_2$. Then it accelerates again by $f_1$ afterwards.
prove if $f_2t_2>2f_1t_1$, the particle passes through point K for 2 times?
My Work
Since this sum asks about returning to initial position I know that the deceleration $f_2$ continues even after the velocity of particle reached zero causing it to move backwards.
I tried writing an expression for,
Distance Traveled Forward < Distance Traveled Backwards
But this didn't yield the given inequality. Can you please help me to solve this? Thanks!